The six core competencies of mathematics in vocational schools are becoming increasingly important in mathematics learning. The reverse teaching design of vocational school mathematics, which focuses on core competencies, precisely grasps the internal logic of knowledge from a holistic perspective, and designs it on a unit by unit basis. The design process is to infer the starting point from the endpoint. Therefore, how to use reverse thinking in teaching design research in vocational school mathematics teaching under the background of core competencies will be the main content of this article.

With the rapid development of internet technology, online education has become an important trend in the education industry. Especially under the influence of the global COVID-19 epidemic, online teaching has been widely applied and promoted. However, there are also some problems with online teaching, such as a lack of realism and low student engagement. Therefore, exploring the integration of online and offline teaching models has become a hot research topic in the field of education. This article will analyze the reform strategy of integrating online and offline teaching in university mathematics courses, aiming to explore how to improve the teaching effectiveness of university mathematics courses and promote students' learning interest and ability through the integration of online and offline teaching.

As an important component of socialist culture with Chinese characteristics, excellent traditional culture is not only the "cradle" of cultural origin, but also the foundation of advanced socialist culture and ideological and political guidance for students. It is an indispensable part of socialist education. With the advent of the Internet era, it not only poses challenges to the ideological and political education of college students, but also provides opportunities for development. In the new era, by means of new ideas and new methods, integrating fine traditional culture into the course of "Chinese Traditional Flower Arrangement Art" can not only promote the effectiveness and attractiveness of the Chinese traditional flower arrangement art course, but also promote the students' ideological level and recognition of excellent traditional culture, and help students improve their cultural awareness and national self-confidence. Based on this, this article explores the strategy research of integrating cultural confidence into the course of "Traditional Chinese Flower Arrangement Art".

With the development of teaching reform, how to optimize funding and education activities from the perspective of "Great Ideological and Political Education" and improve accuracy has become a focus. From the analysis of the current teaching development situation, the guiding role of ideological and political education in funding precision education activities has been very obvious. To better enhance the effectiveness of funding education, actively optimize the precision of funding education, and innovate the way related activities are carried out, which is an inevitable choice for better education work. Based on this, this article mainly studies the precise methods of funding education under the perspective of "Great Ideological and Political Education", for reference only.

Classical photography, aesthetic beauty, and scientific analysis are related. This article explores composition, light manipulation, and emotion to examine the aesthetic components that characterize classical traditions. Pioneers like Julia Margaret Cameron are revealed from a historical perspective, and Ansel Adams' landscapes are the pinnacle of harmony and majesty. Scientific discoveries illuminate the psychology of authenticity and engagement in the digital age while promoting visual literacy. The timeless influence of artistry in the visual narrative is underscored by classic aesthetics, which connect the past, present, and resound through great works.

The theoretical framework of Production Oriented Approach (POA) proposed by Professor Wen Qiufang has undergone a series of development and improvement, forming a "drive facilitate evaluate" teaching framework system that is guided by output tasks, supported by facilitation activities, led by teachers, and jointly constructed by teachers and students. The "facilitation" link is the core of helping learners achieve goals and achieve output tasks. Based on the ideas and requirements of this theory, the author has designed a series of "facilitation" activities to be applied in advanced English reading classrooms. This article intends to review and reflect on these teaching practice activities, in order to gain a deeper understanding of POA theory.